Can an iPad battery be replaced?

Apple does provide battery service for iPad models that currently have hardware support.

iPad Service & Repair - Apple Support

For devices that were released seven or more years ago, service and hardware support are no longer available. Details of device models that remain eligible can be found here:

Obtaining service for your Apple product after an expired warranty - Apple Support

The tags appended to your iPad suggest that you perhaps have an iPad with iOS10 installed - this most likely being an iPad4. This iPad model is obsolete. If you have an iPad4 or earlier, you will be limited to third-party battery replacement using non-genuine parts.

Before spending any money at all, consider that battery replacement will cause reset of the iPad - erasing all installed Apps. App for 32-bit devices (iPad1-4, iPad mini1) have been withdrawn from the Apple App Store - and are not available for download or reinstallation. As such, this may severely impact the utility and usefulness of older models of iPad.

Consequently, it may be considerably more practical and cost effective for you to consider replacing an older model iPad with a much newer model capable of running iPadOS16. Even the entry-level iPad9 is massively more powerful than older models of iPad - and can run the vast majority of currently available Apps.

Yes, bring it to the nearest Apple Store or Apple authorized repair center - they will provide you with more information, including estimated costs.